Electronic – Does using only 2 phases (400V) in a 3 phase transformer affect anything

Each apartment is connected to one phase, different apartments are connected to different phases with interleaving so that phases are hopefully loaded equally.

Yes.

He calls a serviceman and the serviceman claims the substation transformer feeds such voltages and the only thing he can do is to disconnect the tenant from his phase and connect him to the phase with 215 volts.

Yes.

Is it unequal load on different phases or anything else? Also has the serviceman done the right thing or did he just put extra load on the higher voltage phase and induce risk of distribution failure?

Serviceman did the right thing.*

I think you've answered most of your own question!

The substation is presumably supposed to have some kind of voltage regulator (after all, the transformer has a nonzero output impedance, so voltages sag with load). I assume it's theoretically possible that this could be done on a per-phase basis, but my guess is that they only do it as a 3-phase set, in which case the imbalance is caused by unequal loading.

*caveat: I suppose technically someone should measure the currents out of the transformer, and make sure that the imbalance in currents matches the sag in the voltages. If the currents are about the same but the voltages are not, then it could be a higher-than-normal impedance somewhere in the distribution network.

You are correct that in each winding, the magnetic field varies in phase with the current in the windings. What you're having a problem with is the concept of flux being 'annihilated' at where the cores are joined.

It's helpful here to think about 'magnetic circuits'. Think about a single phase transformer for a moment; the core completes a loop that passes through the windings, so the field from the windings has a closed path. Now think about a three phase transformer. Look at the phase A winding. It has a certain amount of field that needs to be returned from one end of the winding to the other. You could just close it on itself, and do the same with phases B and C, and have three separate single-phase transformers, and it would get the job done, but it would be wasteful of material. Consider that the phase relationship of the currents means that, at any given moment, the fields from phases B and C added together are equal and opposite to that of phase A. It doesn't matter which phase you look at, the fields from the other two add to cancel. You see, where you were surmising that the fields annihilated eachother, what in fact happens is that they complement one another, and provide the right amount of magnetic return path. This lets you use less core material, and so economics dictates that's the way to go.

It's a bit like what happens to the currents in a Y-connected three phase load; the currents sum to zero, but it's not that they annihilate one another, it's that they form balanced return paths for one another.